def jensen_shannnon(prob_distributions, logbase=2):
"""Generalised version of Jensen-Shannon Divergence
Compares two or more probability distributions and returns a distance value.
Distance value is bounded as 0<JSD<log2(n) where n is the number of distributions compared.
Args:
prob_distributions (list): 2 Dimensional list of probability distributions (each row a distribution).
logbase (int): The base of the logarithm used to compute the output.
Returns:
divergence (float): Distance between probability distributions.
"""
prob_distributions = np.array(prob_distributions)
# All equal weights
weights = 1 / len(prob_distributions)
# Left term: entropy of mixture
weight_probs = weights * prob_distributions
mixture = weight_probs.sum(axis=0)
entropy_of_mixture = H(mixture, base=logbase)
# Right term: sum of entropies
entropies = np.array([H(P_i, base=logbase) for P_i in prob_distributions])
weight_entropies = weights * entropies
sum_of_entropies = weight_entropies.sum()
divergence = entropy_of_mixture - sum_of_entropies
return divergence
def jsd(prob_distributions, weights, logbase=math.e):
k = zip(weights, np.asarray(prob_distributions))
wprobs = np.asarray([x * y for x, y in list(k)])
mixture = wprobs.sum(axis=0)
entropy_of_mixture = H(mixture, base=logbase)
# right term: sum of entropies
entropies = np.array([H(P_i, base=logbase) for P_i in prob_distributions])
wentropies = weights * entropies
sum_of_entropies = wentropies.sum()
divergence = entropy_of_mixture - sum_of_entropies
return (divergence)
def JSD(prob_distributions, weights, logbase=2):
# left term: entropy of mixture
wprobs = weights * prob_distributions
mixture = wprobs.sum(axis=0)
entropy_of_mixture = H(mixture, base=logbase)
# right term: sum of entropies
entropies = np.array([H(P_i, base=logbase) for P_i in prob_distributions])
wentropies = weights * entropies
# wentropies = np.dot(weights, entropies)
sum_of_entropies = wentropies.sum()
divergence = entropy_of_mixture - sum_of_entropies
return (divergence)